Hamilton-Jacobi approach for Regge-Teitelboim cosmology
arXiv:2004.01650 · doi:10.1088/1361-6382/ab87d9
Abstract
The Hamilton-Jacobi formalism for a geodetic brane-like universe described by the Regge-Teitelboim model is developed. We focus on the description of the complete set of Hamiltonians that ensure the integrability of the model in addition to obtaining the Hamilton principal function . In order to do this, we avoid the second-order in derivative nature of the model by appropriately defining a set of auxiliary variables that yields a first-order Lagrangian. Being a linear in acceleration theory, this scheme unavoidably needs an adequate redefinition of the so-called Generalized Poisson Bracket in order to achieve the right evolution in the reduced phase space. Further this Hamilton-Jacobi framework also enables us to explore the quantum behaviour under a semi-classical approximation of the model. A comparison with the Ostrogradski-Hamilton method for constrained systems is also provided in detail.
arXiv comment22 pages, no figures
References in corpus (14)
- Geodetic Brane Gravity
- Hamilton-Jacobi formulation for singular systems with second order Lagrangians
- Ostrogradski approach for the Regge-Teitelboim type cosmology
- Wave Function of a Brane-like Universe
- Quantum Gravity of a Brane-like Universe
- From the Embedding Theory to General Relativity in a result of inflation
- Constraint algebra for Regge-Teitelboim formulation of gravity
- Hamilton-Jacobi Approach for First Order Actions and Theories with Higher Derivatives
- First Order Actions: a New View
- Involutive constrained systems and Hamilton-Jacobi formalism
- Quantum modified Regge-Teitelboim cosmology
- Hamiltonian analysis for linearly acceleration-dependent Lagrangians
- Gauge symmetry and Virasoro algebra in quantum charged rigid membrane -- a first order formalism
- Virasoro Algebra for Particles with Higher Derivative Interactions
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